1. Elementary Particles
Instrumentation
Accelerators
Dec 15, 2014

2. First accelerator: cathode ray tube

3. With electron charge q: F = q . Efield electron kinetic energy:
Efield = V / D
With electron charge q:
F = q . Efield
electron kinetic energy:
Ee- =  F dD = q.V
Ee- independent of:
distance D
particle mass
heated
filament
distance D
Potential diffence V

4. ElectronVolt: eV 1 eV = |q| Joules = 1.6 x 10-19 Joules
Energy unit: ElectronVolt: eV
1000 eV = 1 keV = 103 eV
1 MeV = 106 eV
1 GeV = 109 eV
1 TeV = 1012 eV
1 eV = |q| Joules = 1.6 x Joules

5. Wimshurst’s electricity generator, Leidsche Flesschen

6. Van de Graaff accelerator
Vertical construction
is easier as support
of belt is easier
Corona discharge
deposits charge
on belt
Left: Robert van de Graaff
From: Principles of Charged
Particle Acceleration
Stanley Humphries, Jr.,
on-line edition, p. 222.

7. Faraday Cage!
HV = 10 kV
gnd
belt

8. Beam pipe From: Principles of Charged Particle Acceleration
Stanley Humphries, Jr.,
on-line edition, p. 223.

9. Hoogspanning (hoge potentiaal) met: Rumkorffse Klos
transformator
bobine
vonkenzender
Marconi
bobine:
ontsteking voor
explosie motoren

10. high-voltage generator
Practical limit to transformers
Cockcroft-Walton
high-voltage generator
Sir John Douglas Cockroft
Nobel Prize 1951
Ernest Walton
From: Principles of Charged
Particle Acceleration
Stanley Humphries, Jr.,
on-line edition, p. 210

11. Cockroft Walton generator
at Fermilab, Chicago, USA
High voltage = 750 kV
Structure in the foreground:
ion (H-) source

12. Motion of charged particle in magnetic field
Lorentz force:
The speed of a charged particle, and therefore its g, does not change by a static magnetic field

13. Motion of charged particle in magnetic field
If magnetic field direction perpendicular to the velocity:
which can be written as : p = r q B → p = B r
radius of curvature
(p in GeV/c, B in T, r in m,
for 1 elementary charge
unit = x10-19 C,
and obtained using
1 eV/c2 = x10-36 kg
and c = m/s ) D Sh ρ

14. Force on charged particle due to electric and magnetic fields:
perpendicular to
motion: deflection
In direction of
motion -> acceleration
or deceleration
-> For acceleration an electric field needs to be produced:
static: need a high voltage: e.g. Cockroft Walton generator,
van de Graaff accelerator
with a changing magnetic field: e.g. betatron
with a high-frequent voltage which creates an accelerating field across one
or more regions at times that particles pass these regions: e.g. cyclotron
with high-frequency electro-magnetic waves in cavities

15. The cyclotron Top view Side view ~
"Dee": conducting,
non-magnetic box
Top view
Ernest O.Lawrence at the controls
of the 37" cyclotron in 1938,
University of California at Berkeley.
1939 Nobel prize for "the invention
and development of the cyclotron,
and for the results thereby attained,
especially with regard to artificial
radioelements."
(the 37" cyclotron could accelerate
deuterons to 8 MeV)
Constant
magnetic field
Side view ~
r.f. voltage
Speed increase smaller if particles become relativistic:
special field configuration or synchro-cyclotron (uses particle
bunches, frequency reduced at end of acceleration cycle)

16. From: S. Y. Lee and K. Y. Ng, PS70_intro. pdf in: http://physics

17. From: S. Y. Lee and K. Y. Ng, PS70_intro. pdf in: http://physics

18. Superconducting cyclotron (AGOR), KVI, Groningen
Protons up to ~ 190 MeV, heavy ions (C, N, Ar, ...) ~ MeV per nucleon

19. Eindhoven: new cyclotron for isotope production (2002)
IBA Cyclone 30, MeV protons, 350 mA

20. Linear Drift Tube accelerator, invented by R. Wideröe~
Particles move through
hollow metal cylinders in
evacuated tube
r.f. voltage: frequency
matched to velocity particles,
so that these are accelerated
for each gap crossed

21. Linear Drift Tube accelerator, Alvarez type
Metal tank
small antenna injects e.m. energy
into resonator, e.m. wave in tank
accelerates particles when they cross
gaps, particles are screened from e.m.
wave when electric field would decelerate
Particles move through
hollow metal cylinders in
evacuated tube ~
Luis Walter Alvarez
Nobel prize 1968, but not for his work on accelerators:
"for his decisive contributions to elementary particle physics,
in particular the discovery of a large number of resonance states,
made possible through his development of the technique of using
hydrogen bubble chamber and data analysis"

22. Inside the tank of the Fermilab Alvarez type 200 MeV proton linac

23. R.f. cavity with drift tubes as used in the
SPS (Super Proton Synchrotron) at CERN
NB: traveling e.m. waves are used
Frequency = MHz
Max. 790 kW
8MV accelerating voltage

24. Standing waves in cavity:
particles and anti-particles
can be accelerated at the same time
Superconducting cavity for the LEP-II
e+e- collider (2000: last year of operation) t1
"iris" t2
Cavities in cryostat in LEP
The direction of E is indicated

25. Non-superconducting cavity as used in LEP-I.
The copper sphere was used for low-loss temporary storage of the
e.m. power in order to reduce the power load of the cavity

26. Generation of r.f. e.m waves with a klystron
* The electron gun 1 produces a flow of electrons.
* The bunching cavities 2 regulate the speed of the electrons so
that they arrive in bunches at the output cavity.
* The bunches of electrons excite microwaves in the output cavity 3
of the klystron.
* The microwaves flow into the waveguide 4, which transports
them to the accelerator.
* The electrons are absorbed in the beam stop 5.
from

27. Synchrotron : circular accelerator with r.f. cavities
for accelerating the particles and with separate magnets
for keeping the particles on track. All large circular
accelerators are of this type.
Injection
During acceleration
the magnetic field
needs to be
"ramped up".
Focussing magnet
r.f. cavity
Bending magnet
Extracted beam
Vacuum beam line

28. CERN, Geneve

30. During acceleration the magnetic field needs to be "ramped up".
Slow extraction
Fast extraction
of remainder of beam
Fast extraction
of part of beam
SPS used as
injector for LEP
For LHC related
studies
At time of operation of LEP

31. Collider: two beams are collided to obtain a high Centre of Mass (CM) energy.
Colliders are usually synchrotrons (exception: SLAC).
In a synchrotron particles and anti-particles can be accelerated and stored in the same machine (e.g. LEP (e+e-), SppS and Tevatron (proton - anti-proton). This is not possible for e.g. a proton-proton collider or an electron-proton collider.
Important parameter for colliders : Luminosity L
N = L s
number of events /s
cross-section
Unit L: barn-1 s-1 or cm-2 s-1

32. CERN accelerator complex
to Gran-Sasso (730 km)

33. Charged particles inside accelerators and in external beamlines
need to be steered by magnetic fields. A requirement is that
small deviations from the design orbit should not grow without
limit. Proper choice of the steering and focusing fields makes this
possible.
Consider first a charged particle moving in a uniform field
and in a plane perpendicular to the field:
displaced orbit
In the plane a deviation from the design orbit does not grow beyond a certain limit: it exhibits oscillatory behavior. However, a deviation in the direction perpendicular to the plane grows in proportion to the number of revolutions made and leads to loss of the particle after some time.
design orbit

34. required. Possible solution : "weak focusing" with a
To prevent instabilities a restoring force in the vertical direction is
required. Possible solution : "weak focusing" with a
"combined function magnet"
field
component
causes downward
force
Components of magnetic field
parallel to the design orbit plane
force particles not moving in the
plane back to it, resulting in
oscillatory motion1) perpendicular
to plane. The field component
perpendicular to the plane now
depends on the position in the
design orbit plane: the period
of the oscillatory motion1) in this
plane around the design orbit
becomes larger than a single
revolution.
pole
shoe
design orbit
plane (seen
from the side)
pole
shoe
field
component
causes
upward
force
1) "betatron oscillations"

35. Dipoles and quadrupoles in LEP

36. proton-proton collider
Large Hadron Collider LHC:
proton-proton collider
Interaction
point
Bunch size squeezed
near interaction point
Crossing angle to avoid long range beam beam interaction
R ~4 km, E ~ 7 TeV (2x!)  B ~ 7 T!

38. Superconducting magnets: no pole shoes
Current distributions

40. LHC dipoles

41. pp collisions 2) heavy collisions:
A proton is a bag filled with quarks en gluons

42. With van de Graaff accelerator: simple:
E = q V, so E = V eV
From Einstein’s Special Theory on Relativity:
E2 = mo2 c4 + p2c2
With:
= v / c, and the Lorentz factor γ:
relativistic mass mr = γ m0
γ = 1 / sqrt(1- 2), and  = sqrt(γ2 -1) / γ
So: total energy E = m0 c2 sqrt(1+ 2 γ2) [= rest mass eq. + kinetic energy]
= γ m0 c2 = mr c2

43. Remember:
TOTAL energy E2 = mo2 c4 + p2c2
Note ‘restmass’ term and ‘kinetic’ term (squared!)
relativistic mass mr = γ m0
p = m v = γ m0 v (for high energy particles: p = γ m0 c)
γ = 1 / sqrt(1- 2)
For high-energy particles (E >> m0c2):
E2 = mo2 c4 + p2c2 = E2 = p2c2  E = pc  p = E/c

44. Examples: electron: rust mass m0 = 511 keV
With total energy 1 GeV: kinetic energy = 1 GeV
Momentum p: 1GeV/c
Other example: electron with [kinetic] energy of 1 MeV (~1/2 m0 c2)
Total energy ET = 1 MeV keV = 1511 keV
Momentum p follows from ET2 = mo2 c4 + p2c2
Gamma factor γ = ET / moc2
Speed follows from γ = 1 / sqrt(1- 2), and  = sqrt(γ2 -1) / γ